Modal logic

The proof uses modal logic, which distinguishes between necessary truths and contingent truths. A truth is necessary if it cannot be avoided, such as 2 + 2 = 4; by contrast, a contingent truth just happens to be the case, for instance "more than half of the earth is covered by water". In the most common interpretation of modal logic, one considers "all possible worlds". If a statement is true in all possible worlds, then it is a necessary truth. If a statement happens to be true in our world, but is not true in all other worlds, then it is a contingent truth. A statement that is true in some world (n ...

See also:

Gödel's ontological proof, Gödel's ontological proof - Modal logic, Gödel's ontological proof - Axioms, Gödel's ontological proof - Derivation, Gödel's ontological proof - Critique of definitions and axioms

Read more here: » Gödel's ontological proof: Encyclopedia II - Gödel's ontological proof - Modal logic

Two of Kripke's earlier works (A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic) were very influential to modal logic. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke because of his contributions to modal logic. In Semantical Considerations on Modal Logic, published in 1963, Kripke responded to a difficulty with classical quantification theory. The whole motivation for the world-relative approach was to reflect the idea t ...

See also:

Saul Kripke, Saul Kripke - Biography, Saul Kripke - Work, Saul Kripke - Modal logic, Saul Kripke - Naming and necessity, Saul Kripke - Wittgenstein, Saul Kripke - Truth

Read more here: » Saul Kripke: Encyclopedia II - Saul Kripke - Modal logic

Modal logic - Alethic epistemic. Modal logic is most often used for talk of the so-called alethic modalities: "it is necessarily the case that..." or "it is possibly the case that...." These (which include metaphysical modalities and logical modalities) are most easily confused with epistemic modalities (from the Greek episteme, knowledge): "It is certainly true that..." and "It may (given the available information) be true that..." In ordinary speech both modalities are of ...

See also:

Modal logic, Modal logic - Metaphysical and other modalities, Modal logic - Alethic epistemic, Modal logic - Deontic temporal, Modal logic - Interpretations of modal logic, Modal logic - Formal Rules, Modal logic - Development of modal logic, Modal logic - Acknowledgements

Read more here: » Modal logic: Encyclopedia II - Modal logic - Metaphysical and other modalities

Modal logic - Alethic epistemic. Modal logic is most often used for talk of the so-called alethic modalities: "it is necessarily the case that..." or "it is possibly the case that...." These (which include metaphysical modalities and logical modalities) are most easily confused with epistemic modalities (from the Greek episteme, knowledge): "It is certainly true that..." and "It may (given the available information) be true that..." In ordinary speech both modalities are of ...

See also:

Modal logic, Modal logic - Metaphysical and other modalities, Modal logic - Alethic epistemic, Modal logic - Deontic temporal, Modal logic - Interpretations of modal logic, Modal logic - Formal rules, Modal logic - Development of modal logic, Modal logic - A note about intensionality of modal logics, Modal logic - Acknowledgements

Read more here: » Modal logic: Encyclopedia II - Modal logic - Metaphysical and other modalities

In metaphysics (in particular, ontology), the different kinds or ways of being are called categories of being or simply categories. According to the Aristotelian tradition, a being is anything that can be said to be in the various senses of this word. Hence, to investigate the categories of being is to determine the most fundamental senses in which things can be said to be. A category, more precisely, is any of the broadest classes of things - 'thing' here meaning anything whatever that ca ...

Including:

• Category of being - Aristotle's Categories
• Category of being - Categories of being
• Category of being - Physical objects
• Category of being - Minds
• Category of being - Classes
• Category of being - Properties
• Category of being - Relations

Read more here: » Category of being: Encyclopedia - Category of being

In philosophy, ontology (from the Greek ὄν, genitive ὄντος: being (part. of εἶναι: to be) and -λογία: writing about, study of) is the most fundamental branch of metaphysics. It studi ...

Including:

• Ontology - Some basic questions
• Ontology - Concepts
• Ontology - Early history of ontology
• Ontology - Subject relationship object
• Ontology - Body and environment
• Ontology - Being
• Ontology - Social Science
• Ontology - Prominent ontologists

Read more here: » Ontology: Encyclopedia - Ontology

In philosophy, essence is the attribute (or set of attributes) that make an object or substance what it fundamentally is. In grammar, it is a subject's necessary predicate. The notion of essence has acquired many slightly but importantly different shades of meaning throughout the history of philosophy; most of them derive from its use in Aristotle and its evolution within the scholastic tradition. Essence in this sense is contrasted with accident: essential properties are properties that a substance has necessarily; a ...

Including:

• Essence - Buddhism
• Essence - Essentiast

Read more here: » Essence: Encyclopedia - Essence

Philosophers have many differing views on what the fundamental categories of being are. In no particular order, here are at least some items that have been regarded as categories of being by someone or other: Category of being - Physical objects. Physical objects are beings; certainly they are said to be in the simple sense that they exist all around us. So a house is a being, a person's body is a being, a tree is a being, a cloud is a being, and so on. They are beings because, and in ...

See also:

Category of being, Category of being - Aristotle's Categories, Category of being - Other systems of categories, Category of being - Categories of being, Category of being - Physical objects, Category of being - Minds, Category of being - Classes, Category of being - Properties, Category of being - Relations

Read more here: » Category of being: Encyclopedia II - Category of being - Categories of being

Languages differ in how fine distinctions of mood they make. No language would provide markings for all the moods below, although they are all expressible in any language using sufficient phraseology. In language, modality is the subject concerning so-called modal auxiliary verbs like can, must, and should, that are customarily used to modify the meaning of other verbs (which in turn tend to take an infinitive form). Modal verbs express possibility (and impossibility, necessity, contingency, etc.), permissibility (and obligation, pros ...

See also:

Linguistic modality, Linguistic modality - Explanation, Linguistic modality - Form, Linguistic modality - Mood and modality, Linguistic modality - Deontic moods, Linguistic modality - Epistemic moods, Linguistic modality - other moods, Linguistic modality - Bibliography

Read more here: » Linguistic modality: Encyclopedia II - Linguistic modality - Mood and modality

The semantics of autoepistemic logic is based on the expansions of a theory, which have a role similar to models in propositional logic. While a propositional model specifies which atoms are true or false, an expansion specifies which formulae are true and which ones are false. In particular, the expansions of an autoepistemic formula T makes this distinction for every subformula contained in T. This distinction allows T to be ...

See also:

Autoepistemic logic, Autoepistemic logic - Syntax, Autoepistemic logic - Semantics

Read more here: » Autoepistemic logic: Encyclopedia II - Autoepistemic logic - Semantics

Within the Madhyamika school of Mahayana Buddhism, Candrakirti identifies the self as being: an essence of things that does not depend on others; it is an intrinsic nature. The non-existence of that is selflessness. -- Bodhisattvayogacaryācatuḥśatakaṭikā 256.1.7 Indeed the concept of Buddhist Emptiness, is the strong assertion that all phenomena are empty of any essence - demonstrating that anti-essentialism lies at the very root of Buddhist praxis. Therefore, within ...

See also:

Essence, Essence - Buddhism, Essence - Essentiast

Read more here: » Essence: Encyclopedia II - Essence - Buddhism

Ontology has one basic question: "What are the fundamental categories of being?" Different philosophers make different lists of such fundamental categories of being. This highlights one of the problems of the philosophical approach—it relies on continued investigation of categories, and has no clear way to stop asking. In theology, library science and artificial intelligence, in contrast, one typically adopts a relatively stable foundation ontology. This avoids some problems with the philosophical approach which has a larger base of ...

See also:

Ontology, Ontology - Some basic questions, Ontology - Concepts, Ontology - Early history of ontology, Ontology - Subject relationship object, Ontology - Body and environment, Ontology - Being, Ontology - Social Science, Ontology - Prominent ontologists

Read more here: » Ontology: Encyclopedia II - Ontology - Some basic questions

Philosophers have many differing views on what the fundamental categories of being are. In no particular order, here are at least some items that have been regarded as categories of being by someone or other: Category of being - Physical objects. Physical objects are beings; certainly they are said to be in the simple sense that they exist all around us. So a house is a being, a person's body is a being, a tree is a being, a cloud is a being, and so on. They are beings because, and in ...

See also:

Category of being, Category of being - Aristotle's Categories, Category of being - Categories of being, Category of being - Physical objects, Category of being - Minds, Category of being - Classes, Category of being - Properties, Category of being - Relations

Read more here: » Category of being: Encyclopedia II - Category of being - Categories of being

The concept of ontology is generally thought to have originated in early Greece and occupied Plato and Aristotle. Since the word is of Greek origin its current meaning and application are certainly sourced from Greek culture. Aristotle described ontology as "the science of being qua being". The word 'qua' means 'in the capacity of'. According to this theory, then, ontology is the science of being inasmuch as it is being, or the study of beings insofar as they exist. Take anything you can find in the world, and look at it ...

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Ontology, Ontology - Some basic questions, Ontology - Concepts, Ontology - Early history of ontology, Ontology - Subject relationship object, Ontology - Body and environment, Ontology - Being, Ontology - Social Science, Ontology - Prominent ontologists

Read more here: » Ontology: Encyclopedia II - Ontology - Early history of ontology

Schools of subjectivism, objectivism and relativism existed at various times in the 20th century, and the postmodernists and body philosophers tried to reframe all these questions in terms of bodies taking some specific action in an environment. This relied to a great degree on insights derived from scientific research into animals taking instinctive action in natural and artificial settings — as st ...

See also:

Ontology, Ontology - Some basic questions, Ontology - Concepts, Ontology - Early history of ontology, Ontology - Subject relationship object, Ontology - Body and environment, Ontology - Being, Ontology - Social Science, Ontology - Prominent ontologists

Read more here: » Ontology: Encyclopedia II - Ontology - Body and environment

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties; non-classical logics are those that lack one or more of these properties, which are: Law of the excluded middle; Law of noncontradiction; Monotonicity of entailment and Idempotency of entailment; Commutativity of conjunction; De Morgan dual ...

Including:

• Classical logic - Examples of classical logics
• Classical logic - Non-classical logics

Read more here: » Classical logic: Encyclopedia - Classical logic

Axiom S5 is the distinctive axiom of the S5 system of modal logic and says that if possibly necessarily p, then necessarily p. If the modality here is what Alvin Plantinga calls "broadly logical" necessity and possibility, then an argument for the axiom can be given as follows. If possibly necessarily p, then there is a possible world w at which p necessarily holds. Then, it is true at w that p is a broadly logically necessary truth, something whose negation would in a broadly logical s ...

Read more here: » Axiom S5: Encyclopedia - Axiom S5

Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. However the subject is grounded, the task of the logician is the same: to advance an account of valid and fallacious inference to allow ...

Including:

• Logic - Nature of logic
• Logic - Informal formal and symbolic logic
• Logic - Rival conceptions of logic
• Logic - History of logic
• Logic - Relation to other sciences
• Logic - Deductive and inductive reasoning
• Logic - Topics in logic
• Logic - Syllogistic logic
• Logic - Predicate logic
• Logic - Modal logic
• Logic - Deduction and reasoning
• Logic - Mathematical logic
• Logic - Philosophical logic
• Logic - Logic and computation
• Logic - Controversies in logic
• Logic - Bivalence and the law of the excluded middle
• Logic - Implication: strict or material?
• Logic - Tolerating the impossible
• Logic - Is logic empirical?

Read more here: » Logic: Encyclopedia - Logic

"What exists", "What is", "What am I", "What is describing this to me", all exemplify questions about being, and highlight the most basic problems in ontology: finding a subject, a relationship, and an object to talk about. During the Enlightenment the view of René Descartes that "cogito ergo sum" ("I think therefore I am") had generally prevailed, although Descartes himself did not believe the question worthy of any deep investigation. However, Descartes was very religious in his philosophy, and indeed argued that "cogito ergo sum" proved ...

See also:

Ontology, Ontology - Some basic questions, Ontology - Concepts, Ontology - Early history of ontology, Ontology - Subject relationship object, Ontology - Body and environment, Ontology - Being, Ontology - Social Science, Ontology - Prominent ontologists

Read more here: » Ontology: Encyclopedia II - Ontology - Subject relationship object

When considering modality it useful to distinguish between two parts: the dictum: what is said the modus: how it is said (that is, the speaker's cognitive, emotive, and/or volitive attitude about what is said) For example, a sentence could have the following dictum: It is hot outside. This dictum could be paired with various types of modi, such as the following: I think that it is hot outside. I believe that it is hot outsi ...

See also:

Linguistic modality, Linguistic modality - Explanation, Linguistic modality - Form, Linguistic modality - Mood and modality, Linguistic modality - Deontic moods, Linguistic modality - Epistemic moods, Linguistic modality - other moods, Linguistic modality - Bibliography

Read more here: » Linguistic modality: Encyclopedia II - Linguistic modality - Explanation